What is Mathematics: Godel's Theorem and Around

This book is an Hyper-textbook for students in mathematical logic and foundations of mathematics. Contents: Platonism, intuition and the nature of mathematics; Axiomatic Set Theory; First Order Arithmetic; Hilbert's Tenth Problem; Incompleteness Theorems; Around Goedel's Theorem.

This accessible book gives a new, detailed and elementary explanation of the Godel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities.

Besides theory, the historical report and personal stories about the main character and on this book's writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences.